### Computer assisted method for proving existence of periodic orbits

DOI: http://dx.doi.org/10.12775/TMNA.1999.019

#### Abstract

We introduce a method based on the Conley index theory

for proving the existence of a periodic trajectory

in a smooth dynamical system in $\mathbb R^n$

where an attracting periodic orbit is numerically observed.

We apply this method to prove the existence of a periodic orbit

in the Rössler equations, as announced in [< i> Computer assisted proof of the existence of a periodic orbit in

the Rössler equations< /i> ].

for proving the existence of a periodic trajectory

in a smooth dynamical system in $\mathbb R^n$

where an attracting periodic orbit is numerically observed.

We apply this method to prove the existence of a periodic orbit

in the Rössler equations, as announced in [< i> Computer assisted proof of the existence of a periodic orbit in

the Rössler equations< /i> ].

#### Keywords

Conley index; periodic orbit; Rössler equations; isolating neighbourhood; algorithm

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